Linear stability of shallow morphodynamic flows
Linear stability of shallow morphodynamic flows
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DOI：
10.1017/jfm.2021.235
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发表时间：
2020-07
影响因子：
3.7
通讯作者：
Jacob Langham;M. Woodhouse;A. Hogg;J. Phillips
中科院分区：
文献类型：
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作者：
Jacob Langham;M. Woodhouse;A. Hogg;J. Phillips
摘要对于浅层陆面水流模型来说，包括下伏河床演变(地貌动力学)和相关沉积相运动的方程越来越普遍。在相当一般的情况下，我们研究了这些系统的线性稳定性。地貌动力学的幼稚公式，以均匀混合的悬浮泥沙和河床之间的泥沙交换为特征，导致了数学上不适定的控制方程。这可以追溯到弗劳德数为${\textit{Fr}}=1$的线性化系统中的一个奇点，该奇点导致短波长扰动的无限不稳定增长。将被忽视的物理过程包括在内可以恢复良好的适当性。在这方面，湍流动量扩散(涡粘性)和适当参数的推移质输沙分别被证明是足够的。然而，我们证明了这样的模型通常继承了非形态动力学设置所不存在的相关不稳定性。我们的分析的含义被考虑到简单的通用闭合，包括根据泥沙浓度在流体和颗粒行为之间切换的阻力定律。定常地形动力学流动分为两种状态：稀释流和浓缩流。稀释流在低浓度下稳定，浓缩流对浓度扰动总是不稳定。通过计算参数空间中线性模式的增长率，我们详细考察了特定模型参数的影响，包括泥沙可蚀性、涡粘性和推移质通量的选择。这些分析可以用来为工程和地球科学中正在进行的业务模型的发展提供信息。
Abstract It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability properties of these systems in considerable generality. Naive formulations of the morphodynamics, featuring exchange of sediment between a well-mixed suspended load and the bed, lead to mathematically ill-posed governing equations. This is traced to a singularity in the linearised system at Froude number ${\textit {Fr}} = 1$ that causes unbounded unstable growth of short-wavelength disturbances. The inclusion of neglected physical processes can restore well posedness. Turbulent momentum diffusion (eddy viscosity) and a suitably parametrised bed load sediment transport are shown separately to be sufficient in this regard. However, we demonstrate that such models typically inherit an associated instability that is absent from non-morphodynamic settings. Implications of our analyses are considered for simple generic closures, including a drag law that switches between fluid and granular behaviour, depending on the sediment concentration. Steady morphodynamic flows bifurcate into two states: dilute flows, which are stable at low ${\textit {Fr}}$, and concentrated flows which are always unstable to disturbances in concentration. By computing the growth rates of linear modes across a wide region of parameter space, we examine in detail the effects of specific model parameters including the choices of sediment erodibility, eddy viscosity and bed load flux. These analyses may be used to inform the ongoing development of operational models in engineering and geosciences.